Abstract: This paper explores the relativistic behavior of spin-half particles possessing an Electric Dipole Moment (EDM) in a curved space-time background induced by a spiral dislocation. A thorough review of the mathematical formulation of the Dirac spinor in the framework of quantum field theory sets the foundation for our investigation. By deriving the action that governs the interaction between the spinor field, the background space-time, and an external electric field, we establish a framework to study the dynamics of the system. Solving the resulting wave equation reveals a set of coupled equations for the radial components of the Dirac spinor, which give rise to a modified energy spectrum attributed to the EDM. To validate our findings, we apply them to the geometric phase and thermodynamics.